# NCERT Solutions for Class 10 Maths Chapter 13 – Surface Areas and Volumes

These NCERT Solutions for Class 10 Maths Chapter 13-Surface Areas and Volumes are one of the essential study materials for CBSE Class 10 board exams. Our experienced teachers have drafted these NCERT Solutions with the utmost care in a step by step manner to make your preparation for the exam easy and effortless. The Chapter – ‘Surface Areas and Volumes’ has been prepared as per the CBSE NCERT Class 10 Maths Book and CBSE Class 10 Maths Syllabus.

The important concepts which are covered in this Chapter are volume of a cuboid, and it’s surface area, the volume of cube and its surface area, the volume of a cylinder and it’s surface area, the volume of a right circular cone and it’s surface area, the volume of a cube and its surface area, the volume of a sphere and its surface area, volume of a hemisphere and its surface area, volume and surface area of combined solids, and volume and surface area of a frustum. All the questions are drafted to the point and fully accurate. Our NCERT Solutions comprise all relevant diagrams to the answers for all the exercises given at the end of the NCERT CBSE Class 10 Maths Chapter 13.

NCERT Solutions for Chapter 13 are prepared in a simple and easy to understand language. Our smart learning techniques and innovative study methods will make your board exam preparation more fun, interactive and efficient. These complete Class 10 Maths Surface Areas and Volumes solutions help you to become thorough with the Chapter quickly and score more marks in your examination.

NCERT Solutions for Class 10 Maths are the finest revision material to make you stress-free and tension-free during your board exams. We have strictly followed the CBSE and NCERT guidelines strictly. Our Solutions strengthen your conceptual understanding and improve your retention rate. They also keep your doubts clear always.

## CBSE NCERT Class 10 Maths Chapter 13

In NCERT Class 10 Maths Chapter 13 – Surface Areas and Volumes, you will be mainly focusing on surface areas and volumes of cone, cuboid, cube and cylinder. Some of the important topics covered in this Chapter have been discussed below.

**Combination of Solids****Surface Area of a Combination of Solids**

In NCERT Class 10 Maths Chapter 13 – Surface Areas and Volumes, you will learn how to break down a solid and analyse its shape in an easy way. You will also learn how to find the areas of the unknown shapes with known shapes.

**The Volume of Combined Solids**

In this segment of NCERT Solutions for Class 10th Maths Chapter 13 – Surface Areas and Volumes, you will be learning how to find the volumes of complex objects with visualising shapes in a simplified way. The formula for calculating the volume of combined solids has been given below

The volume of combined solids

V(solid) = V(Cone) + V(hemisphere)

**Cuboid and Surface Area**

In this part of NCERT Solutions for Class 10th Maths Chapter 13 – Surface Areas and Volumes, you will be taught how to find out the surface area of a cuboid. You will also understand how it is equal to the sum of the areas of its six rectangular faces. The formula for finding the surface area of a cuboid has been given below.

cuboid = 2(l×b)+2(b×h)+2(l×h)=2(lb+bh+lh)

In this chapter, you will also learn about the cube and its surface area, cylinder and its surface area, right circular cone and its surface area and sphere and it’s surface area.

**Volume of Cube**

Here, in CBSE Class 10 Maths Syllabus, you will learn that all the dimensions of the cube are identical.

Hence, volume = l^{3}

Here, l is the length of the cube of the edge

The volume of a cube = base area×height

**Volume of Cuboid**

This section of the Chapter will teach you in detail about how to calculate the volume of a cuboid. The formula for the same has been given below.

Volume of a cuboid =(base area)×height=(lb)h=lbh

**Volume of Cylinder**

This part of the Chapter deals with learning how to calculate the volume of a cylinder, the formula for which has been given below.

Volume of a cylinder = Base area × its height = (π×r^{2})×h=πr^{2}h

In subsequent parts of Class 10 Maths Surface Areas and Volumes, you will also learn about the volume of a right circular cone, the volume of a sphere, the volume of a hemisphere, and hemisphere and it’s surface area.

**Frustum of a Cone**

Here in CBSE NCERT Class 10 Maths Chapter 13, you will be learning how a plane parallel to base cuts the cone, which is why a cone has two separate parts and which part is called the frustum of a cone. You will also learn to calculate the surface area of a frustum and volume of the frustum.

**Shape Conversion of Solids**

In this segment of NCERT Solutions for Class 10 Maths Chapter 13-Surface Areas and Volumes, you will be learning how one solid is converted into another solid with a different shape either by casting or melting with volume at a constant position.

## NCERT Solutions for Class 10th Maths Chapter 13-Surface Areas and Volumes Exercise-Discussion

Our comprehensive NCERT Solutions for Class Maths Chapter 13- Surface Areas and Volumes has 5 exercises in total with about 37 questions in it. Below is a brief overview of the same.

**Exercise 13.1**

This exercise of CBSE NCERT Class, 10 Maths book, consists of 9 questions. Question 1 is based on the cube, where you will have to find the surface area of the cube. Question 2, 3, 4, 5, 6 and 9 are hemisphere based questions. In which you will have to find the surface area of the given shape. Question 7 is based on the cylinder, in which you have to find the area of the canvas. Question 8 is asked from the topic cylinder, where you will be finding the surface area of the solid. Here some questions are direct questions, and some are application-based questions.

**Exercise 13.2:**

This exercise of NCERT Solutions for Class 10 Maths Chapter 13-Surface Areas and Volumes consist of 8 questions. Question 1, 2 4 and 7 are based on finding the volume of different shapes like the cone, hemisphere, the volume of a cylinder, the volume of a cuboid, the volume of an inverted cone. Most questions in this exercise are application-based questions such as question 2, 3, 4, 5, 6, 7, and 8. In order to solve all these questions correctly, you must be thorough with all concepts of the Chapter.

**Exercise 13.3**

This exercise of NCERT CBSE Class 10 Maths Chapter 13 consists of 9 questions. Question 1, 3 and 4 are based on the height of the cylinder. Here, you will have to find the height of the given objects like a cylinder, platform and cylindrical embankment. Question 1 is a direct question, and question 3 and 4 are application-based questions. Question 2 and 7 are based on the concept of the radius. Where you will have to find the radius of the given shapes. Question 5, 6, 8 and 9 are scenario-based questions

**Exercise 13.4**

This exercise of NCERT CBSE Class 10 Maths Chapter 13, consists of 5 questions in total. Question 1, 4 and 5 are scenario-based. Where you will have to solve the questions based on the given situation. All questions of this exercise cover the topic frustum of a cone.

**Exercise 13.5**

This exercise consists of 7 questions in total. All the questions are scenario-based questions, and they cover topics like length and mass, volume and surface area and frustum of a cone. Here, you will have to read the question thoroughly and then check the shapes mentioned in the question before you start solving the given problems.